Name_________________________________________
Practice—Functions and Their Graphs
List the horizontal shift, vertical shift, vertex, axis of symmetry, whether it’s up, down, fat, skinny, or
standard, domain and range, and graph it. .
1. y   x  2   4
2
a) HS ______
b) VS ______
c) Vertex ______
d) A.S. ______
e) Up or down?
f)
Fat, skinny, or standard?
g) Domain ______
h) Range ______
3
2. y  ( x  2)  3
a)
HS ______
b)
VS ______
c)
Vertex ______
d)
A.S. ______
e)
Up or down?
f)
Fat, skinny, or standard?
g)
Domain ______
h)
Range ______
3. y  2 x  1  4
a)
HS ______
b)
VS ______
c)
Vertex ______
d)
A.S. ______
e)
Up or down?
f)
Fat, skinny, or standard?
g)
Domain ______
h)
Range ______
4. y  2 x 
1
4
2
a)
HS ______
b)
VS ______
c)
Vertex ______
d)
A.S. ______
e)
Up or down?
f)
Fat, skinny, or standard?
g)
Domain ______
h)
Range ______
Determine whether the following is and even or odd function. If neither, then state neither.
5. 𝑓(𝑥) = −𝑥 3 + 𝑥
6. 𝑓(𝑥) = 3𝑥 2 + 11𝑥 − 4
Name_________________________________________
Practice—Functions and Their Graphs--KEY
List the horizontal shift, vertical shift, vertex, axis of symmetry, whether it’s up, down, fat, skinny, or
standard, domain and range, and graph it. .
1. y   x  2   4
2
i)
HS → 2
j)
VS ↑ 4
k) Vertex V(2, 4)
l)
A.S. x = 2
m) Up or down? up
n) Fat, skinny, or standard? Standard
o) Domain (−∞, ∞)
p) Range [4, ∞)
3
2. y  ( x  2)  3
a)
HS ← 2
b)
VS ↑ 3
c)
Vertex None
d)
A.S. None
e)
Up or down? up
f)
Fat, skinny, or standard? Standard
g)
Domain (−∞, ∞)
h)
Range (−∞, ∞)
3. y  2 x  1  4
a)
HS ← 1
b)
VS ↓ 4
c)
Vertex None
d)
A.S. None
e)
Up or down? Up
f)
Fat, skinny, or standard? Skinny
g)
Domain [−1, ∞)
h)
Range [−4, ∞)
4. y  
5
1
x 4
7
2
1
a)
HS → 2
b)
VS ↓ 4
c)
Vertex (2 , −4)
d)
A.S. 𝑥 = 2
e)
Up or down? down
f)
Fat, skinny, or standard? fat
g)
Domain (−∞, ∞)
h)
Range (−∞, −4]
1
1
Determine whether the following is and even or odd function. If neither, then state neither.
5. 𝑓(𝑥) = −𝑥 3 + 𝑥 Odd; symmetric about the origin
6. 𝑓(𝑥) = 3𝑥 2 + 11𝑥 − 4 Neither